Non-interacting Active Particles Research Articles

Effect of initial conditions on current fluctuations in non-interacting active particles

We investigate the effect of initial conditions on the fluctuations of the integrated density current across the origin (x = 0) up to a given time t in a one-dimensional system of non-interacting run-and-tumble particles. Each particle has initial probabilities f+ and f− to move with an initial velocity +v and −v respectively, where v > 0. We derive exact results for the variance (second cumulant) of the current for quenched and annealed averages over the initial conditions for the magnetization and the density fields associated with the particles. We show that at large times, the variance displays a t behavior, with a prefactor contingent on the specific density initial conditions used. However, at short times, the variance displays either linear t or quadratic t 2 behavior, which depends on the combination of magnetization and density initial conditions, along with the fraction f+ of particles in the positive velocity state at t = 0. Intriguingly, if f+=0 , the variance displays a short time t 2 behavior with the same prefactor irrespective of the initial conditions for both fields.

Model predictive control of non-interacting active Brownian particles.

Active matter systems are strongly driven to assume non-equilibrium distributions owing to their self-propulsion, e.g., flocking and clustering. Controlling the active matter systems' spatiotemporal distributions offers exciting applications such as directed assembly, programmable materials, and microfluidic actuation. However, these applications involve environments with coupled dynamics and complex tasks, making intuitive control strategies insufficient. This necessitates the development of an automatic feedback control framework, where an algorithm determines appropriate actions based on the system's current state. In this work, we control the distribution of active Brownian particles by applying model predictive control (MPC), a model-based control algorithm that predicts future states and optimizes the control inputs to drive the system along a user-defined objective. The MPC model is based on the Smoluchowski equation with a self-propulsive convective term and an actuated spatiotemporal-varying external field that aligns particles with the applied direction, similar to a magnetic field. We apply the MPC framework to control a Brownian dynamics simulation of non-interacting active particles and illustrate the controller capabilities with two objectives: splitting and juggling sub-populations, and polar order flocking control.

Current fluctuations in an interacting active lattice gas

We study the fluctuations of the integrated density current across the origin up to time T in a lattice model of active particles with hard-core interactions. This model is amenable to an exact description within a fluctuating hydrodynamics framework. We focus on quenched initial conditions for both the density and the magnetization fields and derive expressions for the cumulants of the density current, which can be matched with direct numerical simulations of the microscopic lattice model. For the case of uniform initial profiles, we show that the variance of the integrated current displays three regimes: an initial rise with a coefficient given by the symmetric simple exclusion process, a cross-over regime where the effects of activity increase the fluctuations, and a large-time behavior with a prefactor that depends on the initial conditions, the Péclet number, and the mean density of particles. Additionally, we study the limit of zero diffusion, where the fluctuations intriguingly exhibit a T 2 behavior at short times. However, at large times, the fluctuations still grow as , with a coefficient that can be calculated explicitly. For low densities, we show that this coefficient can be expressed in terms of the effective diffusion constant D eff for non-interacting active particles.

Active particles in reactive disordered media: How does adsorption affect diffusion?

In this work we study analytically and numerically the transport properties of non-interacting active particles moving on a d-dimensional disordered medium. The disorder is modeled by means of a set of non-overlapping spherical obstacles. We assume that obstacles are reactive in the sense that they react in the presence of the particles in an attractive manner: when the particle collides with an obstacle, it is attached during a random time (adsorption time), i.e., it gets adsorbed by an obstacle; thereafter the particle is detached from the obstacle and continues its motion in a random direction. We give an approximate analytical expression for the effective diffusion coefficient when the mean adsorption time is finite. If the mean adsorption time is infinite the system undergoes a transition from a normal to anomalous diffusion regime. We also show that another transition takes place in the mean number of adsorbed particles: in the anomalous diffusion phase all the particles become adsorbed in the average. We show that the fraction of adsorbed particles, seen as an order parameter of the system, undergoes a second-order-like phase transition, because the fraction of adsorbed particles is not differentiable but changes continuously as a function of a parameter of the model.

Tracer dynamics in one dimensional gases of active or passive particles

We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system—this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show long-time subdiffusion: displacements scale as t 1/4 with a density-dependent prefactor that is independent of tracer type, and differs from the corresponding result for passive-in-passive subdiffusion. In an environment of noninteracting active particles, the passive-in-passive results are recovered at low densities for both active and passive tracers, but transient caging effects slow the tracer motion at higher densities, delaying the onset of any t 1/4 regime. For an active tracer in a passive environment, we find more complex outcomes, which depend on details of the dynamical discretization scheme. We interpret these results by studying the density distribution of environmental particles around the tracer. In particular, sticking of environment particles to the tracer cause it to move more slowly in noninteracting than in interacting active environments, while the anomalous behaviour of the active-in-passive cases stems from a ‘snowplough’ effect whereby a large pile of diffusive environmental particles accumulates in front of an RTP tracer during a ballistic run.

Nonequilibrium grand-canonical ensemble built from a physical particle reservoir

We introduce a nonequilibrium grand-canonical ensemble defined by considering the stationary state of a driven system of particles put in contact with a particle reservoir. When an additivity assumption holds for the large deviation function of density, a chemical potential of the reservoir can be defined. The grand-canonical distribution then takes a form similar to the equilibrium one. At variance with equilibrium, though, the probability weight is "renormalized" by a contribution coming from the contact, with respect to the canonical probability weight of the isolated system. A formal grand-canonical potential can be introduced in terms of a scaled cumulant generating function, defined as the Legendre-Fenchel transform of the large deviation function of density. The role of the formal Legendre parameter can be played, physically, by the chemical potential of the reservoir when the latter can be defined, or by a potential energy difference applied between the system and the reservoir. Static fluctuation-response relations naturally follow from the large deviation structure. Some of the results are illustrated on two different explicit examples, a gas of noninteracting active particles and a lattice model of interacting particles.

Bodies in an interacting active fluid: far-field influence of a single body and interaction between two bodies

Because active particles break time-reversal symmetry, an active fluid can sustain currents even without an external drive. We show that when a passive body is placed in a fluid of pairwise interacting active particles, it generates long-range currents, corresponding to density and pressure gradients. By using a multipole expansion and a far-field constitutive relation, we show that the leading-order behavior of all three corresponds to a source dipole. Then, when two bodies or more are placed in the active fluid, generic long-range interactions between the bodies occur. We find these to be qualitatively different from other fluid mediated interactions, such as hydrodynamic or thermal Casimir. The interactions can be predicted by measuring a few single-body properties in separate experiments. Moreover, they are anisotropic and do not satisfy an action-reaction principle. These results extend previous results on non-interacting active particles. Our framework may point to a path towards self-assembly.

Two-dimensional active motion.

The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

Autonomous Engines Driven by Active Matter: Energetics and Design Principles

Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly.

Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact.

We discuss the notion of the nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the nonequilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system-which agrees with a recently proposed general definition of the chemical potential in nonequilibrium systems in contact-we, generically, find that the chemical potential lacks an equation of state in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure.

Aggregation and sedimentation of active Brownian particles at constant affinity.

We study the motility-induced phase separation of active particles driven through the interconversion of two chemical species controlled by ideal reservoirs (chemostats). As a consequence, the propulsion speed is non-constant and depends on the actual inter-particle forces, enhancing the positive feedback between increased density and reduced motility that is responsible for the observed inhomogeneous density. For hard discs, we find that this effect is negligible and that the phase separation is controlled by the average propulsion speed. For soft particles and large propulsion speeds, however, we predict an observable impact on the collective behavior. We briefly comment on the reentrant behavior found for soft discs. Finally, we study the influence of non-constant propulsion on the sedimentation profile of non-interacting active particles.

Active escape dynamics: The effect of persistence on barrier crossing.

We study a system of non-interacting active particles, propelled by colored noises, characterized by an activity time τ, and confined by a double-well potential. A straightforward application of this system is the problem of barrier crossing of active particles, which has been studied only in the limit of small activity. When τ is sufficiently large, equilibrium-like approximations break down in the barrier crossing region. In the model under investigation, it emerges as a sort of "negative temperature" region, and numerical simulations confirm the presence of non-convex local velocity distributions. We propose, in the limit of large τ, approximate equations for the typical trajectories which successfully predict many aspects of the numerical results. The local breakdown of detailed balance and its relation with a recent definition of non-equilibrium heat exchange is also discussed.